Abstract
A study of the epistemologies of practising research mathematicians provides data with respect to the imaginative narratives (Bruner, 1986) used by these mathematicians when reflecting on their research practices. Unlike the paradigmatic narratives of formal mathematics, imaginative narratives involve the members of the mathematical community in active engagement, collaboratively, together with an acknowledgement of the holistic nature of knowing, thinking and feeling. The theoretical distinction is drawn between a contingent repertoire used within the imaginative mode when researching and the objectivist repertoire used to situate mathematics publicly as impersonal, separate and independent of the human or social. Focusing on the mathematicians’ narratives, attention is drawn to how the mathematicians use transcendental or operational functions to support a simple objectivist stance and this is compared with the complexity of the contingent view couched in metaphoric and analogous reasoning. The chapter ends with a discussion of the implications of this analysis for mathematics education.
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Burton, L. (2007). Mathematicians’ Narratives About Mathematics. In: van Kerkhove, B., van Bendegem, J.P. (eds) Perspectives On Mathematical Practices. Logic, Epistemology, and the Unity of Science, vol 5. Springer, Dordrecht. https://doi.org/10.1007/1-4020-5034-8_9
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